The generator matrix 1 0 1 1 1 X^2+X 1 1 X^3+X^2 1 X^3+X 1 1 1 1 0 1 X^2+X 1 1 1 X^3+X^2 1 X^3+X 1 1 1 0 1 X^2+X 1 1 1 X^3+X 1 X^3+X^2 1 1 1 1 1 0 1 1 X^2+X 1 X^3+X^2 1 X^3+X X X 1 X X X 1 1 1 1 0 X^3 X^3+X^2 0 1 1 1 X 1 1 1 X^3+X^2 X^3+X 1 1 0 1 X+1 X^2+X X^2+1 1 X^3+X^2 X^3+X^2+X+1 1 X^3+X 1 X^3+1 X^2+1 X+1 0 1 X^2+X 1 X^3+X^2+X+1 X^3+1 X^3+X^2 1 X^3+X 1 X^2+1 X^3+X^2+X+1 0 1 X^2+X 1 X+1 X^3+1 X^3+X^2 1 X^3+X 1 X+1 X^2+1 X^3+1 X^3+X^2+X+1 0 1 X^2+X+1 X^2+X 1 X^3+X^2 1 X^3+X 1 X^3+X^2+X X^3+X X^3+X^2+1 X^2+X 0 X^3 0 X^3+X^2 X^3+1 X^2+X+1 X X 1 1 X^3+X^2+X+1 X^3+X^2+X+1 X^3+X^2+1 X X^2+X X+1 X^2+1 X 1 X^3 0 0 0 X^3 0 0 0 0 0 X^3 X^3 0 X^3 X^3 0 0 X^3 X^3 0 X^3 0 X^3 X^3 X^3 X^3 X^3 X^3 0 0 0 0 0 0 X^3 X^3 0 0 X^3 0 X^3 0 X^3 0 X^3 X^3 X^3 X^3 X^3 0 X^3 0 X^3 X^3 0 X^3 X^3 0 X^3 X^3 X^3 0 X^3 0 0 0 0 0 X^3 0 X^3 X^3 0 0 0 0 0 0 0 X^3 0 0 0 0 X^3 X^3 X^3 0 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 0 0 0 X^3 0 X^3 0 0 0 0 X^3 X^3 X^3 0 X^3 X^3 0 X^3 X^3 X^3 X^3 0 0 X^3 0 0 X^3 0 0 X^3 0 X^3 0 0 0 X^3 X^3 X^3 X^3 X^3 0 0 X^3 X^3 X^3 X^3 0 X^3 0 0 0 0 0 0 0 0 0 X^3 0 0 X^3 0 0 0 X^3 X^3 X^3 0 0 0 0 X^3 X^3 0 0 0 0 X^3 X^3 0 0 0 0 X^3 X^3 0 0 0 0 X^3 X^3 X^3 X^3 0 0 X^3 0 0 0 0 0 0 X^3 X^3 0 X^3 X^3 X^3 X^3 X^3 0 X^3 X^3 X^3 X^3 X^3 0 0 X^3 X^3 X^3 0 X^3 X^3 X^3 0 0 0 0 0 0 0 X^3 X^3 X^3 X^3 0 X^3 0 X^3 0 X^3 0 X^3 0 X^3 X^3 X^3 X^3 0 0 0 0 0 X^3 X^3 0 0 0 X^3 X^3 0 0 0 X^3 X^3 X^3 0 X^3 X^3 X^3 0 0 0 X^3 X^3 0 0 X^3 X^3 X^3 0 X^3 X^3 X^3 0 0 X^3 X^3 0 0 X^3 0 X^3 0 X^3 0 0 X^3 0 0 generates a code of length 74 over Z2[X]/(X^4) who´s minimum homogenous weight is 68. Homogenous weight enumerator: w(x)=1x^0+56x^68+172x^69+234x^70+536x^71+235x^72+676x^73+382x^74+612x^75+246x^76+488x^77+166x^78+192x^79+59x^80+4x^81+18x^82+4x^83+8x^84+4x^85+1x^88+1x^92+1x^124 The gray image is a linear code over GF(2) with n=592, k=12 and d=272. This code was found by Heurico 1.16 in 0.5 seconds.